Gallai's path decomposition conjecture for graphs of small maximum degree

TL;DR

This paper proves Gallai's path decomposition conjecture for all connected graphs with maximum degree up to five, confirming the conjecture in this specific class of graphs.

Contribution

The paper establishes the validity of Gallai's conjecture for graphs with maximum degree at most five, expanding the classes of graphs where the conjecture holds.

Findings

Gallai's conjecture holds for graphs with maximum degree ≤ 5

Connected graphs with degree ≤ 5 can be decomposed into at most (n+1)/2 paths

The result extends the known cases where Gallai's conjecture is true

Abstract

Gallai's path decomposition conjecture states that the edges of any connected graph on n vertices can be decomposed into at most (n+1)/2 paths. We confirm that conjecture for all graphs with maximum degree at most five.